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22 October, 08:13

A pension fund has an average duration of its liabilities equal to 15 years. The fund is looking at 5-year maturity zero-coupon bonds and 4% yield perpetuities to immunize its interest rate risk. How much of its portfolio should it allocate to the zero-coupon bonds to immunize if there are no other assets funding the plan?

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  1. 22 October, 09:52
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    The 52 of its portfolio should be allocated to the zero-coupon bonds to immunie if there are no other assets funding the plan.

    Explanation:

    the duration of the perpetuity = (1+YTM) / YTM

    = (1+0.04) / 0.04

    = 26 years

    the weights of the bonds = w

    5*w + 26 * (1-w) = 15

    5*w + 26 - 26*w = 15

    21*w = 11

    w = 0.52

    Therefore, The 52 of its portfolio should be allocated to the zero-coupon bonds to immunie if there are no other assets funding the plan.
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